Some Combinatorial Properties of Hook Lengths, Contents, and Parts of Partitions

This paper proves a generalization of a conjecture of Guoniu Han, inspired originally by an identity of Nekrasov and Okounkov. The main result states that certain sums over partitions p of n, involving symmetric functions of the squares of the hook lengths of p, are polynomial functions of n. A similar result is obtained for symmetric functions of the contents and shifted parts of n.Comment: 20 pages. Correction of some inaccuracies, and a new Theorem 4.

Brazilian elections: voting for a scaling democracy

The proportional elections held in Brazil in 1998 and 2002 display identical statistical signatures. In particular, the distribution of votes among candidates includes a power-law regimen. We suggest that the rationale behind this robust scaling invariance is a multiplicative process in which the voter's choice for a candidate is governed by a product of probabilities.Comment: 4 pages, 2 figure

Generation of ultrashort electrical pulses in semiconductor waveguides

We report a novel device capable of generating ultrashort electrical pulses on a coplanar waveguide (CPW) by means of optical rectification. The device consists of a completely passive GaAs-based optical waveguide, which is velocity matched to a CPW line. Optical pulses are injected into the device and electrical pulses are collected at the output. Experimental results obtained in the laboratory show the potential of this device for high speed optical-to-electrical conversion

Design, fabrication, and characterization of deep-etched waveguide gratings

One-dimensional (1-D) deep-etched gratings on a specially grown AlGaAs wafer were designed and fabricated. The gratings were fabricated using state-of-the-art electron beam lithography and high-aspect-ratio reactive ion etching (RIE) in order to achieve the required narrow deep air slots with good accuracy and reproducibility. Since remarkable etch depths (up to 1.5 /spl mu/m), which completely cut through the waveguide core layer, have been attained, gratings composed of only five periods (and, thus, shorter than 6 /spl mu/m) have a bandgap larger than 100 nm. A defect was introduced by increasing the width of the central semiconductor tooth to create microcavities that exhibit a narrow transmission peak (less than 7 nm) around the wavelength of 1530 nm. The transmission spectra between 1460 and 1580 nm have been systematically measured, and the losses have been estimated for a set of gratings, both with and without a defect, for different periods and air slot dimensions. Numerical results obtained via a bidirectional beam propagation code allowed the evaluation of transmissivity, reflectivity, and diffraction losses. By comparing experimental results with the authors' numerical findings, a clear picture of the role of the grating's geometric parameters in determining its spectral features and diffractive losses is illustrated

Studies of Salt Water intrusion in Opobo/Nkoro Rivers State Using Geophysical and Hydrochemical Methods

Salt water intrusions into fresh water aquifers in Opobo town in Nkoro L.G.A, Rivers state is becoming an issue of concern to the community, and as such requires detailed analysis through an integration of qualitative (geo-electric) and quantitative (hydrochemical) methods. Twenty vertical electrical soundings (VES) labelled as O/MSC/01 to O/MSC/20 and three 2D electrical resistivity tomography (ERT) data were acquired in the area. Results from interpretation of the twenty VES profiles showed 4 geo-electric layers, which are topsoil, sand, sandy clay and clay. In VES geo-electric sections, it was observed that salt intrusions occur at depths of 43.135m, 55.20m, 43.528m, 51.63m, and 28.357m along O/MSC/02, O/MSC/05, O/MSC/07, O/MSC/11 and O/MSC/15 profiles respectively. No salt intrusion was observed in O/MSC/01, O/MSC/04, O/MSC/09, O/MSC/10, O/MSC/12 and O/MSC/14 within the depth investigated. Results of 2D imaging along VES profiles 10, 11 and 12, show salt intrusions observed along the three profiles at different depths within the subsurface. Along profile O/MSC/10, saltwater intrusions (with resistivity range of 59.2Ωm-60.1Ωm) was observed at depth of 7.59-9.59m at lateral distance of 34.0-36.0m and depth of 5.59-7.59m at lateral distance of 94-96m. Along profile O/MSC/11 salt intrusions (with resistivity range of 58.8Ωm-59.2Ωm) was observed at depth of 2.59-5.59m at lateral distance of 28-40m, and 110-128m, while along profile O/MSC/12 salt intrusions (with resistivity range of 14.5-20Ωm) was observed at depth of 3.59-5.59m at lateral distance of 112-118m. These findings were not observed in VES surveys along similar profiles where 2D ERT was carried out. 3D map computed to connect aquifers within the third geo-electric layers for VES points 1-20, showed that within the third geo-electric layers for O/MSC/02, 05, 07, 11, 16, 17, and 20 lies saline water. The reliability of these results was validated by results from quantitative assessment of physiochemical parameters (PH, electrical conductivity (EC), and total hardness) and hydrochemical contents (HCO3-, Na+, K+, CL-, and SO42-) used to evaluate the ionic abundance of water samples taken from seven wells/boreholes in the area. PH values of 6.40-6.90 were predominant in the samples which indicates slight acidity and unsuitable for human consumption, EC values in the order of 1705μS/cm, & 1853.74μS/cm were obtained and total dissolved Solids (TDS) was in the order of 700.30mg/l & 750.02mg/l. Elevated EC values in water is indicative of high ionic abundance, and is diagnostic to salinity of the water as reflected in the 1D and 2D geo-electric surveys. However, the study area also contains fresh water aquifers lying within the third geo-electric layers for VES profiles O/MSC/01, 03, 06, 08, 09, 10, 12, and 18, hence a water supply tube well can be drilled in these areas for groundwater production but the water should be subjected to hydrochemical test to ascertain its level of contamination and prior treatments before human consumption. Keywords: Saltwater Intrusion, Groundwater, Vertical electrical sounding (VES), Electrical resistivity  tomography (ERT), Geo-electric section

Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations

We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective movement of tracer particles driven by a pressure difference between two fixed sites (''wells'') separated by Euclidean distance r. For strongly correlated pore networks at criticality, we find that the probability distribution functions P(l) and P(t) follow the same scaling Ansatz originally proposed for the uncorrelated case, but with quite different scaling exponents. We relate these changes in dynamical behavior to the main morphological difference between correlated and uncorrelated clusters, namely, the compactness of their backbones. Our simulations reveal that the dynamical scaling exponents for correlated geometries take values intermediate between the uncorrelated and homogeneous limiting cases

Politics, Political Competition, and the Political Budget Cycle in Canada, 1870–2000: A Search Across Alternative Fiscal Transmission Mechanisms

In this paper Engel-Granger time series methodology is used to combine trending economic variables with stationary political factors to search for well-defined political influences on central government budgets in Canada over the entire post-Confederation time period from 1870 to 2000. To motivate such an inquiry we first investigate and find evidence of partisan political influence on Canada’s macro aggregates. However, because politics can influence economic outcomes only if there is a transmission mechanism through actual public policy choices, our finding of cycles in real output growth begs the question of whether such cycles arise through fiscal policy. Our analysis of three main fiscal policy instruments - public non-interest expenditure, taxation and the deficit net of interest - gives little support to any current political theory of public budgets, but does support the hypothesis that the degree of political competition matters for policy choices in both the long and short run. This new channel for the influence of politics on economic policy has not previously been isolated empirically in Canada and poses new questions in trying to reconcile the previous mixed results with respect to the influence of politics on economic aggregates

Self-consistent Ornstein-Zernike approximation for three-dimensional spins

An Ornstein-Zernike approximation for the two-body correlation function embodying thermodynamic consistency is applied to a system of classical Heisenberg spins on a three-dimensional lattice. The consistency condition determined in a previous work is supplemented by introducing a simplified expression for the mean-square fluctuations of the spin on each lattice site. The thermodynamics and the correlations obtained by this closure are then compared with approximants based on extrapolation of series expansions and with Monte Carlo simulations. The comparison reveals that many properties of the model, including the critical temperature, are very well reproduced by this simple version of the theory, but that it shows substantial quantitative error in the critical region, both above the critical temperature and with respect to its rendering of the spontaneous magnetization curve. A less simple but conceptually more satisfactory version of the SCOZA is then developed, but not solved, in which the effects of transverse correlations on the longitudinal susceptibility is included, yielding a more complete and accurate description of the spin-wave properties of the model.Comment: 32 pages, 12 figure

Critical Exponents for Nuclear Multifragmentation: dynamical lattice model

We present a dynamical and dissipative lattice model, designed to mimic nuclear multifragmentation. Monte-Carlo simulations with this model show clear signature of critical behaviour and reproduce experimentally observed correlations. In particular, using techniques devised for finite systems, we could obtain two of its critical exponents, whose values are in agreement with those of the universality class to which nuclear multifragmentation is supposed to belong.Comment: 10 pages, 3 figures, to be published in Nuclear Physics

Do Departures from Democratic Accountability Compromise the Stability of Public Finances? Keynesianism, Central Banking, and Minority Governments in the Canadian System of Party Government, 1867 – 2009

This paper is concerned with the effectiveness of Westminster parliamentary institutions in ensuring the stability of a nation's public finances. Our starting point and major hypothesis is that the governance structure embodied in Canada's parliamentary system has contributed importantly to the maintenance of fiscal stability. The fact that the Government of Canada, like the central government of many other modern democracies, has survived for over a century without default on its public debt means that in some meaningful sense, long run responsibility with respect to the nation's finances has in fact been achieved, and we show that this is in fact the case. Hence a more meaningful test of our main hypothesis requires the designation of specific sub-periods when the ideological background for political policy making changed and/or when the institutions and organizations for operationalizing policy varied in ways that either improved or discouraged responsible fiscal performance. We consider ideational and institutional factors that are predicted to either enhance or detract from accountability and fiscal stability, including central banking, the adoption of Keynesianism, inflation targeting and periods of minority government, and test for their effects on long run stability of the debt to GDP ratio using data for almost the entire history of the modern state from 1867 to 2008